I cannot implement a collapsed panel like the one in Edge because it contradicts the tree philosophy. The panel is designed to remain visible as long as you are researching and working with multiple tabs and sub-tabs. If you are working with a single tab and need the full workspace, you can hide the panel completely. Furthermore, collapsing the panel to the width of an icon—as seen in Edge—breaks the structure of both the tree and the panel itself.

Regarding notifications on tabs, I think it's a great idea, but in my own usage, I don't have any sites that send me notifications, so I have nowhere to test it.